SI3 (Sea Ice modelling Integrated Initiative) is the sea ice engine of NEMO (Nucleus for European Modelling of the Ocean). It is adapted to regional and global sea ice and climate problems. It is intended to be a flexible tool for studying sea ice and its interactions with the other components of the Earth System over a wide range of space and time scales. For these applications, a 2+1D continuum approach is currently the most appropriate, SI3 is based on the Arctic Ice Dynamics Joint EXperiment (AIDJEX) framework, combining the ice thickness distribution framework, the conservation of horizontal momentum, an elastic-viscous plastic rheology, and energy-conserving halo-thermodynamics. Prognostic variables are the two-dimensional horizontal velocity field, ice volume, area, enthalpy, salt content, snow volume and enthalpy, and melt pond volume and area. In the horizontal direction, the model uses a curvilinear orthogonal grid. In the vertical direction, the model uses equally-spaced layers. In thickness space, the model uses thickness categories with prescribed boundaries. Various physical and numerical choices are available to describe sea ice physics. SI3 is interfaced with the NEMO ocean engine, and, via the OASIS coupler, with several atmospheric general circulation models. It also supports two-way grid embedding via the AGRIF software.